Parametric Bilinear Generalized Approximate Message Passing

We propose a scheme to estimate the parameters bi and cj of the bilinear form zm = Σi,j bizm(i,j) cj from noisy measurements {ym}mM=1, where ym and zm are related through an arbitrary likelihood function and zm(i,j) are known. Our scheme is based on generalized approximate message passing (G-AMP): it treats bi and cj as random variables and zm(i,j) as an i.i.d. Gaussian 3-way tensor in order to de...